Variational charge relaxation in ionic crystals: An efficient treatment of statics and dynamics

An ab initio variationally induced breathing (VIB) description of the energetics and dynamics of ionic crystals is developed within the spherical-ion-pair approximation and the Gordon-Kim ansatz. In the VIB method, the total crystal charge density is given by the overlap of Kohn-Sham ionic charge densities. Spherical charge deformation of the ions is accomplished by adding an effective many-body crystal site potential to the atomic potential used in the Kohn-Sham procedure. Parameters defining this effective site potential are treated variationally such that the total crystal electronic energy is a minimum for a given structural configuration. We have explored a number of forms of the effective potential, including Watson-sphere types where both the charge and radius of the sphere are variationally determined. In addition, we have investigated anion-cation charge transfer by incorporating an additional variational parameter. We also present a formulation of the lattice dynamics of ionic crystals based on the VIB prescription in which the electronic variational parameters are treated as dynamical variables within the adiabatic approximation. With the computed phonon density of states, the structural parameters of a crystal can then be determined at any temperature and pressure (or stress condition) by mini- mizing the quasiharmonic Gibbs free energy with respect to the structural parameters along the electronic adiabatic surface. The complete pressure- and temperature-dependent thermal and elastic properties of a crystal can also be determined. We have applied the VIB procedure to calculate the equations of state, elastic properties, phonon dispersion relations, and phase stability of the alkaline earth oxides (MgO, CaO, and SrO). The calculated properties are generally in quite good agreement with experiment. Spherical charge deformation within the ionic description is responsible for a considerable improvement over rigid-ion elastic constants and bulk moduli, but some of the remaining discrepancies cannot in principle be eliminated within a spherical-ion model. In particular, the effect of spherical breathing on the optical vibrational frequencies is not dramatic and further improvement (e.g., reduction of LO-TO splitting) will require the inclusion of nonspherical charge relaxation (polarizability).